Find all the values of x in the interval [0, 2pie] that satisfy the equation 2cos(x) + sin(2x) = 0.

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Find all the values of x in the interval [0, 2pie] that satisfy the equation 2cos(x) + sin(2x) = 0.

Mathematics
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step one is to rewrite \[sin(2x)=2sin(x)cos(x)\]
then you get \[2cos(x)+2cos(x)sin(x)=0\] \[2cos(x)(1+sin(x))=0\] \[cos(x)=0\] or \[1+sin(x)=0\] \[sin(x)=-\frac{1}{2}\]
can you solve from there?

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Other answers:

can you continue please?
sure. you are in the interval \[(0,2\pi)\]
in that interval cosine is 0 at \[\frac{\pi}{2}\] and \[\frac{3\pi}{2}\]
are those fractions?
if you do not instantly know where \[sin(x)=-\frac{1}{2}\] then look at the cheat sheet http://tutorial.math.lamar.edu/cheat_table.aspx and see that it is at \[\frac{7\pi}{6}\] and \[\frac{11\pi}{6}\]
that is where the second coordinate is \[-\frac{1}{2}\]
unit circle on last page of cheat sheet

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